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A DIRECT RECONSTRUCTION ALGORITHM FOR THE ANISOTROPIC INVERSE CONDUCTIVITY PROBLEM BASED ON CALDERÓN'S METHOD IN THE
Rashmi Murthy1, Yi-Hsuan Lin2, Kwancheol Shin3
1Department of Mathematics, University of Helsinki, Finland.
Abstract:
A direct reconstruction algorithm based on Calderón's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic inverse conductivity problem, the entries of the unperturbed anisotropic tensors are assumed known a priori, and it remains to reconstruct the multiplicative scalar field. The quasi-conformal map in the plane facilitates the Calderón-based approach for anisotropic conductivities. The method is demonstrated on discontinuous radially symmetric conductivities of high and low contrast.
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